Skip to main content
SpringerLink
Log in

Stability analysis of double-walled and triple-walled carbon nanotubes having local curvature

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this study, stability loss research has been made for composite material containing a locally curved one double-walled carbon nanotube and one triple-walled carbon nanotube separately. The research has been made within the scope of piecewise-homogenous body model by the use of three-dimensional linearized theory of stability (TDLTS). The carbon nanotubes are resistant to tension, but as they contain large gaps in their structure, their resistance to compression is very low. For this reason, searching the behaviors of nanotubes under compression is very important. The van der Waals forces between the walls of the carbon nanotube have been considered. It has been thought that the referred composite material is under the effect of uniformly distributed normal forces in the direction of carbon nanotube at infinity. In the model, ideal contact conditions have been used between the nanotube and the matrix. In addition, the effect of increasing the number of layers of the nanotube on the critical load has been investigated. The results obtained from this study will be able to guide in the implementations relevant to modeling of mechanical behaviors of the addressed composite material. Thus, the limits required to be considered in the production of composite material containing double-walled and triple-walled nanotubes with local curvature have been obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Availability of data and materials

Data and material are available upon request.

Code availability

Software application or custom codes are available upon request.

References

  1. Coban, F.: The stress distribution of infinite body containing a single locally curved and hollow fiber. Master Thesis, Yıldız Technical University (2009)

  2. Akbarov, S.D., Kosker, R., Çoban, F.: Theoretical limit of fracture under compression of unidirectional low density composites having hollow and locally curved fibers. XVIII. National Mechanics Congress. Manisa. pp. 10–20 (2013)

  3. Tekercioğlu R (2006) The surface stability loss of the viscoelastic half-space covered with the stack of layers. Dissertaton, Yıldız Technical University

  4. Babich, I.Y., Guz, A.N., Shul’ga, N.A.: Study of the dynamics and stability of composite materials in a three-dimensional formulation. Sov. Appl. Mech. 18, 3–27 (1982)

    MATH  Google Scholar 

  5. Babich, I.Y., Guz, A.N.: Stability of fibrous composites. Appl. Mech. Rev. 45, 60–80 (1992)

    Google Scholar 

  6. Babich, I.Y., Guz, A.N., Chekhov, V.N.: The three-dimensional theory of stability of fibrous and laminated materials. Int. Appl. Mech. 37, 1103–1141 (2001)

    MATH  Google Scholar 

  7. Chung, I., Weitsman, Y.J.: Model for micro-buckling/micro-kinking compressive response of fiber-reinforced composites. Appl. Mech. Rev. 47, 256–261 (1994)

    Google Scholar 

  8. Budiansky, B., Fleck, N.A.: Compressive failure of fibre composites. J. Mech. Phys. Solids 41(1), 183–211 (1993)

    Google Scholar 

  9. Budiansky, B., Fleck, N.A.: Compressive kinking of fiber composites: a topical review. Appl. Mech. Rev. 47(6S), 246–250 (1994)

    Google Scholar 

  10. Rosen, B.W., Dow, N.F., Hashin, Z.: Mechanical Properties of Fibrous Composites. General Electric Co, Philedelpia (1965)

    Google Scholar 

  11. Dow, N.F., Gruntfest, I: Determination of most needed potentially possible ımprovements in materials for ballistic and space vehicles. General Electric Co, Space Sciences Laboratory, TIS R60SD389 (1960)

  12. Schuerch, H.: Prediction of compressive strength in uniaxial boron fiber-metal matrix composite materials. AIAA J. 4(1), 102–106 (1966)

    Google Scholar 

  13. Kyriakides, S., Perry, E.J., Liechti, K.M.: Instability and failure of fiber composites in compression. Appl. Mech. Rev. 47, 262–268 (1994)

    Google Scholar 

  14. Hermann, L.R., Mason, W.E., Chan, S.T.: Response of reinforcing wires to compressive states of stress. J. Compos. Mater. 1, 212–226 (1967)

    Google Scholar 

  15. Karpenko, L.I., Terletskii, V.A., Lyashenko, B.: A mechanism of the failure of oriented plastic. Strength Mater. 4, 50–56 (1972)

    Google Scholar 

  16. Rosen, B.W., Dow, N.F.: Mechanics of failure of fibrous composites. Fract. H. Liebowitz Ed. Academic Press. vol. 7, pp. 611–674 (1972).

  17. Guz, A.N.: Determination of the theoretical compressive strength of reinforced materials. Dokl Akad Nauk Ukr SSR, Ser A Phys-Math Sci 3, 236–238 (1969)

    Google Scholar 

  18. Guz, A.N.: Construction of a theory os stability of undirectional fiber composites. Sov Appl Mech 5, 62–70 (1969)

    Google Scholar 

  19. Guz, A.N.: Mechanics of Fracture of Composite Materials in Compression. Naukova Dumka, Kiev (1990)

    Google Scholar 

  20. Kosker, R.: Some problems about internal stability loss and stress distribution in an elastic and viscoelastic unidirected fibrous composites. Dissertation, Yıldız Technical University (2002)

  21. Akbarov, S.D.: Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites. Springer, Berlin (2012)

    Google Scholar 

  22. Hutchens, S.B., Needleman, A., Greer, J.R.: Analysis of uniaxial compression of vertically aligned carbon nanotubes. J. Mech. Phys. Solids 59(10), 2227–2237 (2011)

    MATH  Google Scholar 

  23. Jia, J., Zhao, J., Xu, G., et al.: A comparison of the mechanical properties of fibers spun from different carbon nanotubes. Carbon 49(4), 1333–1339 (2011)

    Google Scholar 

  24. Yeh, M.K., Hsieh, T.H., Tai, N.H.: Fabrication and mechanical properties of multi-walled carbon nanotubes/epoxy nanocomposites. Mater. Sci. Eng., A 483–484, 289–292 (2006)

    Google Scholar 

  25. Yeh, M.K., Tai, N.H., Lin, Y.J.: Mechanical properties of phenolic-based nanocomposites reinforced by multi-walled carbon nanotubes and carbon fibers. Compos Part A Appl Sci Manuf 39(4), 677–684 (2008)

    Google Scholar 

  26. Mezghani, K., Farooqui, M., Furquan, S., Atieh, M.: Influence of carbon nanotube (CNT) on the mechanical properties of LLDPE/CNT nanocomposite fibers. Mater Matters 65, 3633–3635 (2011)

    Google Scholar 

  27. Zhang, X.L., Liu, Z.B., Zhao, X., et al.: Nonlinear optical properties of hydroxyl groups modified multi-walled carbon nanotubes. Chem. Phys. Lett. 494(1–3), 75–79 (2010)

    Google Scholar 

  28. Wang, Q.: Torsional buckling of double-walled carbon nanotubes. Carbon 46(8), 1172–1174 (2008)

    Google Scholar 

  29. Wu, C.L., Lin, H.C., Hsu, J.S., Yip, M.C., Fang, W.: Static and dynamic mechanical properties of polydimethylsiloxane/carbon nanotube nanocomposites. Thin Solid Films 517, 4895–4901 (2009)

    Google Scholar 

  30. Kalamkarov, A.L., Georgiades, A.V., Rokkam, S.K., et al.: Analytical and numerical techniques to predict carbon nanotubes properties. Int. J. Solids Struct. 43(22–23), 6832–6854 (2006)

    MATH  Google Scholar 

  31. Xiaohu, Y., Qiang, H.: Investigation of axially compressed buckling of a multi-walled carbon nanotube under temperature field. Compos Sci. Technol. 67(1), 125–134 (2007)

    Google Scholar 

  32. Zhbanov, A.I., Pogorelov, E.G., Chang, Y.C.: Van der Waals interaction between two crossed carbon nanotubes. ACS Nano 4, 5937–5945 (2010)

    Google Scholar 

  33. Li, C., Chou, T.W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40(10), 2487–2499 (2003)

    MATH  Google Scholar 

  34. Ru, C.Q.: Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube. J. Appl. Phys. 87, 7227–7231 (2008)

    Google Scholar 

  35. Guz, A.N., Lapusta, Y.N.: Three-dimensional problems of the near-surface instability of fiber composites in compression (model of a piecewise-uniform medium) (survey). Int. Appl. Mech. 35, 641–670 (1999)

    MATH  Google Scholar 

  36. Guz, A.N., Dekret, V.A.: Plane problems of stability of composite materials with a finite size filler. Mech. Compos. Mater. 36, 77–86 (2000)

    Google Scholar 

  37. Shima, H.: Buckling of Carbon Nanotubes: A State of the Art Review. Materials, Basel (2012)

    Google Scholar 

  38. Wu, S.J., Ho, Y.H., Chang, C.P., Lin, M.F.: Electronic properties of armchair carbon nanotube array. Phys. E 32, 581–584 (2006)

    Google Scholar 

  39. Yang, Y., Zhang, L., Lim, C.W.: Wave propagation in fluid-filled single-walled carbon nanotube on analytically nonlocal EulerBernoulli beam model. J. Sound Vib. 7, 1567–1579 (2012)

    Google Scholar 

  40. Wang, L.: Vibration analysis of nanotubes conveying fluid based on gradient elasticity theory. JVC/J. Vib Control 18(2), 313–320 (2012)

    MathSciNet  MATH  Google Scholar 

  41. Shokrieh, M.M., Rafiee, R.: Investigation of nanotube length effect on the reinforcement efficiency in carbon nanotube based composites. Compos. Struct. 10, 2415–2420 (2010)

    Google Scholar 

  42. Georgantzinos, S.K., Giannopoulos, G.I., Anifantis, N.K.: Investigation of stress-strain behavior of single walled carbon nanotube/rubber composites by a multi-scale finite element method. Theor. Appl. Fract. Mech. 3, 158–164 (2009)

    Google Scholar 

  43. Baykasoğlu, C., Kırca, M., Muğan, A.: Investigation of fracture behavior of carbon nanotubes containing reconstructed atomic space.II. Nanotechnology Congress. pp. 48–54 (2012)

  44. Fu, Y., Bi, R., Zhang, P.: Nonlinear dynamic instability of double-walled carbon nanotubes under periodic excitation. Acta Mechanica Solida Sin 22, 206–212 (2009)

    Google Scholar 

  45. Ansari, R., Gholami, R., Sahmani, S., Norouzzadeh, A., Bazdid-Vahdati, M.: Dynamic stability analysis of embedded multi-walled carbon nanotubes in thermal environment. Acta Mechanica Solida Sin 28, 659–667 (2015)

    Google Scholar 

  46. Ru, C.Q.: Column buckling of multiwalled carbon nanotubes with interlayer radial displacements. Phys Rev B - Condens Matter Mater Phys. 62, 16962–16969 (2000)

    Google Scholar 

  47. Shen, H.S.: Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure. Int. J. Solids Struct. 41(9–10), 2643–2657 (2004)

    MATH  Google Scholar 

  48. Thai, H.T.: A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 52, 56–64 (2012)

    MathSciNet  MATH  Google Scholar 

  49. Jochum, C., Grandidier, J.C.: Microbuckling elastic modelling approach of a single carbon fibre embedded in an epoxy matrix. Compos Sci. Technol. 64(16), 2441–2449 (2004)

    Google Scholar 

  50. Lourie, O., Cox, D.M., Wagner, H.D.: Buckling and collapse of embedded carbon nanotubes. Phys. Rev. Lett. 81(8), 1638–1645 (1998)

    Google Scholar 

  51. Young, R.J., Kinloch, I.A., Gong, L.: The mechanics of graphene nanocomposites: a review. Compos. Sci. Technol. 72(12), 1459–1476 (2012)

    Google Scholar 

  52. Guz, I.: Continuum solid mechanics at nano-scale: how small can it go. J. Nanomater Mol. Nanotechnol. (2012). https://doi.org/10.4172/jnmn.1000e103

    Article  Google Scholar 

  53. Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. Adv. Appl. Mech. 42, 1–68 (2009)

    Google Scholar 

  54. Windle, A.H.: Two defining moments: a personal view by Prof. Alan H. Windle. Compos. Sci. Technol. 67(5), 929–930 (2007)

    Google Scholar 

  55. Harik, V.M.: Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods. Solid State Commun. 120(7–8), 331–335 (2001)

    Google Scholar 

  56. Guz, A.N., Rushchidsky, J.J.: Nanomaterials: on the mechanics of nanomaterials. Int. Appl. Mech. 39, 1271–1293 (2003)

    Google Scholar 

  57. Guz, A.N., Rushchidsky, J.J.: Short Introduction to Mechanics of Nanocomposites. Scientific Academic Publishing, USA (2012)

    Google Scholar 

  58. Ru, C.Q.: Axially compressed buckling of a double walled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265–1279 (2001)

    MATH  Google Scholar 

  59. Murmu, T., Pradhan, S.C.: Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Phys. E 41, 1232–1239 (2009)

    Google Scholar 

  60. Barrettaa, R., Marotti de Sciarraa, F., Vaccaro, M.S.: On nonlocal mechanics of curved elastic beams. Int. J. Eng. Sci. 144, 1–17 (2019)

    MathSciNet  Google Scholar 

  61. Barrettaa, R., Fabbrocinob, F., Lucianoc, R., Marotti de Sciarraa, F., Rutad, G.: Buckling loads of nano-beams in stress-driven nonlocal elasticity. Mech. Adv. Mater. Struct. 27(11), 869–875 (2020)

    Google Scholar 

  62. Barrettaa, R., Canadija, M., Marotti de Sciarraa, F.: Modified nonlocal strain gradient elasticity for nano-rods and application to carbon nanotubes. Appl. Sci. 9, 514 (2019). https://doi.org/10.3390/app9030514

    Article  Google Scholar 

  63. Akbarov, S.D.: Microbuckling of a double-walled carbon nanotube embedded in an elastic matrix. Int. J. Solids Struct. 50(16–17), 2584–2596 (2013)

    Google Scholar 

  64. Akbarov, S.D., Guz, A.N.: Method of solving problems in the mechanics of fiber composites with curved structures. Sov. Appl. Mech. 20, 777–790 (1985)

    MATH  Google Scholar 

  65. Akbarov, S.D., Guz, A.N.: Mechanics of Curved Composites. Kluwer Academic Publishers, Dordrecht (2000)

    MATH  Google Scholar 

  66. Guz, A.N.: Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies. Springer, Berlin (1999)

    MATH  Google Scholar 

  67. Akbarov, S. D., Kosker, R., Şimsek, K.: On the Theoretical strength limit in compression of viscoelastic unidirectional fibrous composites materials. In: International fracture conference. Kocaeli. pp. 791–800 (2005)

Download references

Funding

This study has been supported by Yıldız Technical University Scientific Research Projects Coordination Department. Project Number: 2013-07-03-DOP01.

Author information

Authors and Affiliations

  1. Faculty of Chemical and Metallurgical Engineering, Yıldız Technical University, Istanbul, Turkey

    Fatma Çoban Kayıkçı

  2. Department of Mathematical Engineering, Yıldız Technical University, Istanbul, Turkey

    Reşat Köşker

Authors
  1. Fatma Çoban Kayıkçı
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reşat Köşker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatma Çoban Kayıkçı.

Ethics declarations

Conflict of interest

There are no confilcts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Çoban Kayıkçı, F., Köşker, R. Stability analysis of double-walled and triple-walled carbon nanotubes having local curvature. Arch Appl Mech 91, 1669–1681 (2021). https://doi.org/10.1007/s00419-020-01846-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01846-5

Keywords

Search

Navigation